Related papers: Discrete chain graph models
We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate…
The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
This note presents a simple proof of the monotonicity of the invariant distribution of a discrete Markov chain with a finite state space. This answers a question recently raised by David Siegmund.
The conditionally Markov (CM) sequence contains different classes including Markov, reciprocal, and so-called $CM_L$ and $CM_F$ (two special classes of CM sequences). Each class has its own forward and backward dynamic models. The evolution…
Adaptive Markov chains are an important class of Monte Carlo methods for sampling from probability distributions. The time evolution of adaptive algorithms depends on past samples, and thus these algorithms are non-Markovian. Although there…
The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of…
A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted…
We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
We consider the irreducibility of switch-based Markov chains for the approximate uniform sampling of Hamiltonian cycles in a given undirected dense graph on $n$ vertices. As our main result, we show that every pair of Hamiltonian cycles in…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such…
We present several new results on the feasibility of inferring the hidden states in strongly-connected trackable weak models. Here, a weak model is a directed graph in which each node is assigned a set of colors which may be emitted when…